How to interpret investment risk and return

Every investment is presented with a number: “returned 12% this year”, “pays IPCA + 6%”, “rose 40% in three years”. The number is real, but on its own it does not tell you whether the investment is good for you, or how much you could lose along the way.

This article explains how to read both sides of the equation, risk and return, and which questions to ask before comparing alternatives. The numerical examples are hypothetical and serve only to illustrate the calculations. Nothing here recommends a product or portfolio.

Return: which number are we talking about

Return is the gain or loss on an investment over a period, usually expressed as a percentage of the amount invested. The CVM’s “Introduction to Investments” handbook (the CVM is Brazil’s securities regulator) distinguishes two moments: when you invest, you only have the expected return, what you hope to earn; the return actually obtained is known only when you redeem.

Before comparing two numbers, check four things.

Nominal or real. The nominal return is what appears on the statement. The real return discounts inflation. If an investment returned 10% in a year when inflation was 4%, the gain in purchasing power is not 6%, but 1.10 ÷ 1.04 − 1 ≈ 5.77%. The reason is explained in Inflation: causes, measures and consequences.

Cumulative or annual. “Returned 30% in three years” is not the same as 10% a year. Because gains build on earlier gains, the equivalent annual rate is (1.30)^(1/3) − 1 ≈ 9.14% a year. The logic of interest on interest is in Compound interest: how it works in practice.

Gross or net. Management fees, custody fees, brokerage and taxes come out of the return. Two products with the same gross return can deliver different amounts to your pocket. Basic taxation of fixed income and equities in Brazil is covered in Fixed income and equities: risks and features.

Which period. A return measured over a favorable window can look much better than one measured over another. The same CVM handbook reminds readers: “Past performance is no guarantee of future performance.”

Risk: the chance that the result differs from the expected

The CVM defines risk, in finance, as “the chance that the return obtained on an investment differs from the one expected”. The SEC, the US market regulator, uses a similar definition on Investor.gov: risk is the degree of uncertainty or potential financial loss inherent in an investment decision.

Note that the definition includes both directions. An asset that can rise a lot usually can also fall a lot. The CVM handbook groups risks as follows:

Type of risk	What it is
Market	Price fluctuation due to interest rates, inflation, exchange rates, growth, politics or the business itself
Credit	The issuer of a debt security not paying interest or principal
Liquidity	Not being able to sell quickly at a fair price
Legal	A legal flaw that prevents exercising the rights of the security or contract
Operational	Failures of systems, equipment or people in trading, custody or settlement

Investor.gov adds other names for similar risks, such as inflation risk (inflation eroding the purchasing power of those receiving fixed interest) and interest rate risk (a bond’s price falling when interest rates rise, if you sell before maturity). The case of Brazilian government bonds is detailed in Tesouro Direto: bonds, rates and risks.

How risk is usually measured

There is no single risk number. Three measures appear frequently in investment materials.

Volatility. This is how much returns fluctuate around the average, usually measured by the standard deviation of returns. It was Harry Markowitz’s approach; his 1952 work treated a portfolio’s risk through the variance of returns, according to the press release for the 1990 Nobel Prize in Economic Sciences. The limitation: volatility measures fluctuation; it does not measure the risk of default or of being unable to sell.

Maximum drawdown. This is the largest peak-to-trough decline observed in a track record. It answers a practical question: how far would I have seen my balance fall at the worst moment?

Credit rating. For debt securities, rating agencies assign grades according to the chance that the issuer will not pay. The CVM handbook explains that each agency uses its own scale and that, in general, the letter A indicates the best rating.

Same average, different results

An illustrative example shows why looking only at the average is misleading. Imagine two hypothetical investments over four years:

Year	Investment A	Investment B
1	+8%	+30%
2	+8%	−20%
3	+8%	+25%
4	+8%	−3%
Simple average of returns	8%	8%
Cumulative result	+36.05%	+26.10%

Both have the same arithmetic average, 8% a year. But R$ 1,000 in A would become R$ 1,360.49 (1.08 to the fourth power), while in B it would become R$ 1,261.00 (1.30 × 0.80 × 1.25 × 0.97). Fluctuation by itself reduced the compound result. And anyone who needed to redeem at the end of the second year would have R$ 1,040 in B, against R$ 1,166.40 in A.

The math of losses

Percentage losses and gains do not offset each other in the same proportion:

Decline	Gain needed to return to the initial value
10%	11.1%
20%	25%
50%	100%
100%	No recovery possible

A 50% drop turns R$ 1,000 into R$ 500; to get back to R$ 1,000, the R$ 500 must double. In equities, the CVM notes on its Investor Portal that it is possible to lose the entire amount invested. And in fixed income too, according to the same page, “it is possible to have negative returns”.

The relationship between risk and return

The CVM handbook sums up the logic with an example: if two assets had the same risk and one paid more, everyone would buy the one that pays more, and prices would adjust until the difference disappeared. That is why, in practice, riskier assets tend to offer higher expected returns. Investor.gov says the same: the greater the risk, the greater the return investors demand to accept it.

Two cautions when using this rule:

• It applies to the expected return, not the return obtained. Taking on more risk means accepting a wider range of possible outcomes, including bad ones. In a hypothetical example, an investment with a 50% chance of returning +20% and a 50% chance of returning −10% has an expected return of 0.5 × 20% + 0.5 × (−10%) = 5%. An investment that returns 5% with near certainty has the same expected return, but very different risk.
• The converse does not hold. High risk does not guarantee high returns. And a promise of high returns with low risk is a warning sign: the CVM recommends being suspicious of returns “far out of line with market reality”, which may conceal fraud. See Digital financial scams: how to avoid them and how to react.

Liquidity and time horizon count too

Liquidity is how easily an investment can be turned into cash at a fair price. The CVM treats return, risk and liquidity as the three basic dimensions of any investment. For an emergency fund, for example, the Investor Portal says return is the least important: the priority is low risk and high liquidity.

The time horizon also changes how risk should be read. Investor.gov notes that those with a long horizon may feel more comfortable with more volatile investments, while those with a short horizon may prefer less fluctuation. The reason is simple: with little time, a decline may coincide with the moment you need the money.

Your side of the equation: risk profile

The same fluctuation may be acceptable to one person and unacceptable to another. The CVM handbook separates two dimensions:

• capacity to take risk, which depends on the share of your wealth at stake and your stage of life. Losing R$ 1,000 weighs much more for someone who has only that R$ 1,000 than for someone with R$ 10,000 saved;
• willingness to take risk, which is your personal comfort with seeing your balance fluctuate. This is where the usual classifications come from: conservative, moderate and aggressive.

In Brazil, this is grounded in regulation. CVM Resolution 30, of 2021, prohibits intermediaries and advisers from recommending products without checking whether they are suitable for the client’s profile, a process known as suitability. The check must consider, at a minimum, the client’s objectives (time horizon, risk preference and purpose), financial situation (income, wealth and future need for funds) and knowledge of the product’s risks. The rule also requires considering direct and indirect costs and avoiding recommending anything with excessive cost for that profile.

The profile questionnaire is a starting point, not a guarantee. Investor.gov warns that online questionnaires may be biased in favor of the products of whoever offers them. And, under CVM Resolution 30, an outdated profile prevents a recommendation: it is worth updating it when your situation changes.

Questions to ask when you see a number

Before comparing alternatives, the editorial team suggests this checklist:

1. Is the return nominal or real? Gross or net of costs and taxes?
2. Is it cumulative or annual? Over what period was it measured?
3. How far has the investment fallen at the worst point in the available history?
4. Who is the issuer and what happens if it does not pay? Is there any guarantee?
5. Can I redeem when I need to? At what price?
6. If the result is bad, how much of my wealth is at stake?

One way to reduce part of the risk without giving up all of the expected return is to combine different investments. That is the subject of Diversification: benefits and limits.

Key takeaways

• Risk is the chance that the result differs from the expected, upward or downward. It takes several forms: market, credit, liquidity, legal and operational.
• A return figure only makes sense with context: real or nominal, annual or cumulative, net or gross, and over which period.
• Higher expected returns usually come with higher risk, but nothing guarantees the return. Your time horizon, your emergency fund and your comfort with losses determine how much risk fits your situation.